The traditional method of teaching children how to count and do arithmetic is inadequate for three essential reasons: 1) the child needs to memorize numerous names for numbers bigger than nine and the nomenclature used for naming these numbers partially hides the similarity of the numbers, e.g., one, ten, hundred, thousand, etc., which are the units of counting in base ten; 2) no useful manipulative objects or concepts are used to teach arithmetic, e.g. the multiplication table is still memorized using brut force or flash cards at best; and 3) no sense of the order of magnitude for large or small number is given to the child.
The following U.S. patents disclose kits, tools or apparatus which try to alleviate one or more of the three above mentioned inadequacies, but none of them deals with all three inadequacies in a satisfactory manner. In particular, items 1) and 3) above are not practically dealt with at all, and the manipulative objects proposed for item 2) deal either only with one digit addition and subtraction or, when dealing with multiple-digit arithmetic, are too difficult and complex to be of general use.
U.S. Pat. No. 4,504,234 to Jarvis discloses a device useful for teaching the concept of squares, cubes, and roots. Smaller square or rectangular pieces are detachably secured to the array 13 by a hook and loop fastener.
U.S. Pat. No. 4,548,585 to Kelly discloses ten shapes, each distinctive of an integer from one to ten and each being distinctively colored. The shapes of at least some of the integers can be placed together in a composite shape which is the same as the shape of the larger integer to which the smaller integers add up.
U.S. Pat. No. 4,585,419 to Rinaldelli discloses an aid for teaching number systems of any base. For the base 10, unit cubes are used to fill up a first box, and ten such filled boxes are used to make up a larger box, and so on. The same can be done with number systems based on other numbers, but different size boxes must be used. For example, for counting in the base 2, the smallest box contains two unit cubes, the next larger box contains two of the smaller boxes, and so on.
U.S. Pat. No. 234,247 to Classen discloses an apparatus for teaching arithmetic having blocks D, E and F of three orders of magnitude (in the base 10). These blocks are used with one another to represent figures as shown in FIG. 1 where the numbers 146 and 67 are added. Blocks representing each of the numbers are positioned directly above or below the associated number in spaces provided in the apparatus. The blocks in the spaces below the second number are then placed in the spaces above the first number to illustrate the addition of the units.
U.S. Pat. No. 846,485 to Leitch discloses the use of different colors in teaching arithmetic and numerical values.
U.S. Pat. No. 2,663,096 to McCurdy discloses an educational toy including blocks made in various lengths from a size one unit long to a size ten units long. An error control blueprint is a sheet marked with squares or rectangles which correspond exactly in size with the unit sizes of the blocks, thereby indicating the correct pattern for stacking the blocks from the ten-unit length up to the one-unit length.
U.S. Pat. No. 3,002,295 to Armstrong discloses a device for teaching number concepts which includes an arithmetic answerboard which is lineated into a plurality of square spaces which define a plurality of vertically extending rows. A series of blocks or movable members can be positioned on the board, the blocks being of various lengths, from one to ten units, corresponding in size to the spaces on the board. The spaces on the board are numbered from bottom to top such that the number in each space represents the number of spaces below that space and, therefore, the number of block units which would cover the spaces below that space. For example, in row 20A, the space having the numeral 1 is exposed indicating that one unit block is positioned on the board below that space. The elements in each row 20 of spaces on the board are of different colors from the first to the tenth row, and the color cycle can repeat itself from the eleventh to the twentieth row. Furthermore, only one space in the first row is colored, two elements in the next row are colored, and so on progressively across the board. The blocks, which are divided into spaces equal to the spaces on the board, can be colored to correspond with a particular row on the board. Furthermore, various blocks can be placed in one row and the total number of units in the blocks will be reflected in the empty space above the top block in the row. Subtraction, multiplication and division can also be taught using the device.
U.S. Pat. No. 3,125,814 to Walcuk discloses a counting device including unit elements, tens elements, and hundreds elements, wherein the hundreds elements are stackable to represent one thousand in three dimensions.
U.S. Pat. No. 4,382,794 to Preus discloses an instructional aid consisting of a plurality of objects each corresponding to an integer between one and ten and having a thickness representing the number to which it corresponds. In addition to integers, a plurality of objects of different shapes are provided, a characteristic of the shape of each object corresponding to an integer between one and ten. The objects have distinctive colors, including combinations of colors representing the factors of the integer, where the integer is not a prime number. Moreover, the English name of the integer or the integer with which a shape is associated is provided on the integer or shape.